Those arrested include 37 suspected "Islamist militants" and hundreds of potential criminals who previously had warrants out against them, as well as several hundred ordinary arrests, Bangladeshi police said on Saturday.

"We have arrested 3,155 people ... as part of the special drive over the last 24 hours," A K M Shahidur Rahman, deputy police inspector general, told the AFP news agency.

"The militants included 27 members of Jamayetul Mujahideen Bangladesh," he added, referring to one one of the main domestic outlawed groups blamed partly for the attacks by the Bangladeshi government.

None of those arrested as part of the crackdown is believed to be "a high-level operator" who might have organised or ordered attacks, police told the Associated Press news agency. All the detainees are being held in jail.

The sweeping crackdown came as Prime Minister Sheikh Hasina vowed to hunt down the killers.

"It may take time, but God willing, we will be able to bring them under control," Hasina told a meeting of her ruling Awami League party on Saturday.

"Where will the criminals hide? Each and every killer will be brought to book as we did after the 2015 mayhem," she said, referring to a deadly transport blockade last year organised by opposition parties.

'Ordinary and innocent people'

However, opposition parties immediately accused the police of using the crackdown to suppress political dissent.

"Hundreds of opposition activists have been arrested in the police drive," Fakhrul Islam Alamgir, secretary-general of the Bangladesh Nationalist Party (BNP), told AFP.

"In the name of the crackdown against Islamist militants, many ordinary and innocent people are being detained."

Hasina has accused the BNP and the country's largest Islamist party, Jamaat-e-Islami, of orchestrating the attacks after they failed to topple the government in last year's transport blockade.